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Simplifying (5x + 8y)(5x + 8y) = 0 Multiply (5x + 8y) * (5x + 8y) (5x * (5x + 8y) + 8y * (5x + 8y)) = 0 ((5x * 5x + 8y * 5x) + 8y * (5x + 8y)) = 0 Reorder the terms: ((40xy + 25x2) + 8y * (5x + 8y)) = 0 ((40xy + 25x2) + 8y * (5x + 8y)) = 0 (40xy + 25x2 + (5x * 8y + 8y * 8y)) = 0 (40xy + 25x2 + (40xy + 64y2)) = 0 Reorder the terms: (40xy + 40xy + 25x2 + 64y2) = 0 Combine like terms: 40xy + 40xy = 80xy (80xy + 25x2 + 64y2) = 0 Solving 80xy + 25x2 + 64y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + 8y)(5x + 8y) = 0Subproblem 1
Set the factor '(5x + 8y)' equal to zero and attempt to solve: Simplifying 5x + 8y = 0 Solving 5x + 8y = 0 Move all terms containing x to the left, all other terms to the right. Add '-8y' to each side of the equation. 5x + 8y + -8y = 0 + -8y Combine like terms: 8y + -8y = 0 5x + 0 = 0 + -8y 5x = 0 + -8y Remove the zero: 5x = -8y Divide each side by '5'. x = -1.6y Simplifying x = -1.6ySubproblem 2
Set the factor '(5x + 8y)' equal to zero and attempt to solve: Simplifying 5x + 8y = 0 Solving 5x + 8y = 0 Move all terms containing x to the left, all other terms to the right. Add '-8y' to each side of the equation. 5x + 8y + -8y = 0 + -8y Combine like terms: 8y + -8y = 0 5x + 0 = 0 + -8y 5x = 0 + -8y Remove the zero: 5x = -8y Divide each side by '5'. x = -1.6y Simplifying x = -1.6ySolution
x = {-1.6y, -1.6y}
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